LOS ANGELES, Feb 7 (Reuters) - Film director Woody Allen denied the recent accusations of his adopted daughter that he molested her when she was 7, insisting in an open letter on Friday that the allegation was fabricated by her mother, actress Mia Farrow, with whom he was then fighting a custody battle.

The response by Allen, 78, to the accusations of sexual assault by Dylan Farrow, now 28, was published on the New York Times' website five days after she gave the newspaper her own account that repeated and elaborated on those allegations.

"I did not molest Dylan," Allen wrote. "I loved her and hope one day she will grasp how she has been cheated out of having a loving father and exploited by a mother more interested in her own festering anger than her daughter's well-being." (Reporting by Steve Gorman; Editing by Ken Wills)